German Published Patent Application No. 199 08 352 discloses a fuel-injection method for an internal combustion engine in which the fuel is supplied from the fuel tank into a storage chamber with the aid of an electric fuel pump and a post-connected high-pressure pump. The pressure generated in the storage chamber is measured using a pressure sensor. The system is controlled and regulated to a setpoint value of the pressure in the storage chamber. According to this reference, a fault in the fuel-supply system is detected by a plausibility check. Once a fault is detected in the fuel-supply system, a diagnostic cycle of the internal combustion engine is initiated in which diagnostic functions are activated that check the individual components of the fuel-supply system with respect to their operability. Among others, an electrical check of the high-pressure sensor is implemented by evaluating the output signals of the pressure sensor. In the process, it is ascertained whether the output signal assumes values within a permitted range, and it is checked whether the time characteristic of the output signal has a typical profile as a function of the fuel-supply system. If one of these two conditions is not satisfied, a defect or a fault of the pressure sensor is assumed. In response to the detected fault of the pressure sensor, the fault is indicated by means of a display device, and an operation for emergency conditions of the internal combustion engine is triggered at the same time. The operation under emergency conditions may be implemented such that the pressure regulation is shut off, so that the pressure in the storage chamber is set solely by the pressure-precontrol.